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Modified Multistep Quasi-Newton Method And Its Convergence

Posted on:2013-01-12Degree:MasterType:Thesis
Country:ChinaCandidate:J YuFull Text:PDF
GTID:2230330362971135Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
Quasi-Newton method is one of the efficient algorithms for solving unconstrained optimizationproblems. In multistep quasi-Newton methods the extended quasi-Newton equation is generated basedon the interpolatory polynomials utilizing information from more than one previous steps. Thecoefficients in combination of displacement and the gradient difference may be negative in the generalmultistep method, which may not make good results. In this paper, a modified multistepquasi-Newton method is proposed, the coefficients in combination of displacement and the gradientdifference are non-negative, and their sum is1. Hence we develop the modified multistepquasi-Newton method. And we prove the convergence of the new algorithm and carry out thenumerical experiments.The paper is divided into five chapters. The first chapter briefly introduces methods for solvingunconstrained optimization and the development of multistep quasi-Newton methods. The secondchapter describes multistep quasi-Newton methods, and we give several typical kinds of multistepquasi-Newton methods. In the third chapter we develop the modified multistep quasi-Newton methodbased on typical multistep quasi-Newton methods of the previous chapter, and prove its convergenceunder some conditions. In the fourth chapter we carry out numerical comparison experiments aboutthe algorithms in Chapter3, analyze numerical results, and draw useful conclusions. The theoretic andnumerical results show that the algorithm in this paper is efficient and promising.
Keywords/Search Tags:Unconstrained optimization, Quasi-Newton equation, Quasi-Newton method, multistepmethod, Convergence
PDF Full Text Request
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